Scotus and univocity

I call a concept 'univocal' if it has that sameness of meaning which is required so that to affirm and deny it of the same subject amounts to a contradiction; also, if it has that sameness of meaning required such that it can function as a middle term in a syllogistic argument - thus that where two terms are united in a middle

1 Catherine Pickstock, 'Modernity and Scholasticism: A Critique of Recent Invocations of Univocity', forthcoming in Antonianum. I am grateful to Dr Pickstock for allowing me sight of this paper in proof form.

term having this sameness of meaning, the inference does not fail by the fallacy of equivocation.2

So says Duns Scotus, as if with clarity: indeed, on one level what he says is clear, for at face value this definition of univocity is simply a restatement of the Aristotelian dictum latinised in much medieval discussion as eadem est scientia oppositorum3 - you can know what it is to affirm something only if you know what would count as its negation; they are one and the same 'knowledge'. For if what you deny does not have the same meaning as what I affirm, then the denial does not contradict what is affirmed. As Anselm pointed out in his Proslogion, unless the fool, who says there is no God, agrees with the theist, who says God exists, about what to say 'God exists' means, then the atheist does not deny what the theist affirms, and may not be an atheist at all.4 More simply, if I say that there is a cat on the mat and you say there is no cat on the mat, you contradict what I say if and only if we mean the same thing by there being a cat on the mat; otherwise you do not deny what I say. Hence, Scotus says, 'p' is univocally predicated so long as 'p' and '~p' are contradictories.

From this follows Scotus' second way of defining 'univocity'. Since a valid syllogistic inference justifies the relating of two terms to each other (the 'extremes') through their common relation to a third term (the 'middle term'), such validity can be secured only if the middle term has the same sense when related to the two extremes. Hence, the inference 'If every man is mortal, and if Socrates is a man, then Socrates is mortal' is valid only if 'man' has the same meaning in both antecedents; it would be an invalid inference if, for example, 'man' in the first antecedent had the gendered meaning in English of 'male' and had the generic meaning of 'human' in the second. For even if, as it happens, the consequent is true (Socrates being a male human), it would not follow as a conclusion from the antecedents, and the inference would be invalid.

That might seem clear enough, but in fact it is not in the least clear.5 For what Scotus proposes as his second definition of univocity is, as far as this explanation goes, in fact but a condition of deductively inferential validity which depends upon, and is not itself a definition of, the univo-cal predication of terms. For of course we cannot know that a deductive inference is valid unless we know that the middle term is predicated uni-vocally in both antecedents; hence we cannot know that the middle term

5 An unusual occurrence in Scotus, who more frequently seems every bit as obscure as he is.

is univocally predicated from the fact that the inference is valid. To say, as Scotus does, that 'univocity' of meaning is that possessed by such middle terms as are required for deductive validity is to beg the question: the determination of validity presupposes criteria for the determination of univocity, not the other way round.6

It might seem, nonetheless, that all is not lost, since it would appear that even without this second criterion we can fall back on Scotus' first criterion for univocity: if a term is univocal then to affirm and deny it of the same subject amounts to a contradiction. As we shall see, however, this criterion too is contestable as a definition of univocity, stating conditions both necessary and sufficient. For Scotus' account gives only a necessary condition, and in any case prima facie there appear to be counter-examples: there are terms, predicated of the same subject, the affirmation and denial of which are genuine contradictories, even though the affirmation and denial are related only analogically. But much argument is required before that case can be made.

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